Question

In the following exercises, translate to a system of equations and solve.

Nancy bought seven pounds of oranges and three pounds of bananas for \(17. Her husband later bought three pounds of oranges and six pounds of bananas for \)12. What was the cost per pound of the oranges and the bananas?

Short answer

The cost of orange is $2 and cost of banana is $1

Step-by-step solution

Step 1. Given Information  

The given data is that Nancy bought seven pounds of oranges and three pounds of bananas for $17. Her husband later bought three pounds of oranges and six pounds of bananas for $12.

Step 2. Explanation 

Let the cost of orange be x and cost of banana be y.

The cost of seven pounds of oranges and three pounds of bananas for $17 that is $7x+3y=17--\left(1\right)$

The cost of three pounds of oranges and six pounds of bananas for $12 that is$3x+6y=12--\left(2\right)$

Step 3. Calculation 

Rewrite the equation (1) by multiplying it with 2.

$$\begin{gathered} 2(7x+3y)=2\left(17\right) \\ 14x+6y=34--\left(1\right) \end{gathered}$$

Solve the equation (2) and (3) by subtracting equation (2) from equation (3).

$$\begin{gathered} 14x+6y-3x-6y=34-12 \\ 11x=22 \\ x=2 \end{gathered}$$

Substitute the value of x in equation (1) and simplify.

$$\begin{gathered} 7\left(2\right)+3y=17 \\ 14+3y=17 \\ 3y=3 \\ y=1 \end{gathered}$$